A Common Root

Algebra Level 3

There are three real values of b for which the equations:

2x2+5x+2b=02{ x }^{ 2 }+5x+2b=0 and 2x3+7x2+5x+1=02{ x }^{ 3 }+7{ x }^{ 2 }+5{ x }+1=0 have at least one common root.

The sum of these three values for b can be expressed in the form mn\frac { m }{ n } , where m and n are coprime positive integers.

Find m+nm+n.

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